A block of mass m kg is connected to two strings as shown. If T1 = √ 3T2,

Question

A block of mass m kg is connected to two strings as shown. If \(T_1 = \sqrt{3}T_2,\) then choose correct option

(1) \(\theta _1 = 60^\circ ,\ \theta _2 = 30^\circ ,\ T_1 = \frac{mg}{2}\)

(2) \(\theta _1 = 60^\circ,\ \theta _2 = 30^\circ,\ T_2 = \frac{mg}{2}\)

(3) \(\theta _1 = 30^\circ,\ \theta _2 = 60^\circ,\ T_1 = \frac{3mg}{4}\)

(4) \(\theta _1 = 30^\circ,\ \theta _2 = 60^\circ ,\ T_2 = \frac{3mg}{4}\)

Answer 1

Correct option is : (2) \(\theta _1 = 60^\circ,\ \theta _2 = 30^\circ,\ T_2 = \frac{mg}{2}\)

\(T_2\cos \theta _2 = T_2 \cos \theta _1\)

\(T_2\cos\theta _2 = \sqrt{3}T_2\cos\theta _1\)

\(\cos\theta _2 = \sqrt{3}\cos\theta _1\)

\(\theta _1 = 60^\circ, \theta _2 = 30^\circ\)